How do I copy OpenOffice document files from a Debian Etch PC, to a Windows Vista laptop?

Umm, more info please? What do you mean exactly by "copy", and just where are you having problems?

At the very least you need to save/export the files to an MS Office supported .doc format, assuming you want to be able to open them in that program. Of course that won't be a a problem if you're using OO.o in Windows too.

I want to be able to work on a Document file, while on my Windows Vista laptop; a file that is presently on my Linux PC.

Still it is not clear what the real problem is, hence I try to guess:

1) if the problem is to transfer files from a linux system to a windows system, it depends on which protocols you are permitted to use for exchanging data. Maybe the easy way is to temporarily enable your linux machine to accept SSH/SCP connections (that is to open port 22 in the firewall rules) and use a free opensource program in windows to establish this connection: WinSCP.

2) if the problem is to manage open office files using microsoft word, you can either save them as .doc in openoffice (as David the H. already suggested) or you can install the office plugin to open ODF files. It is available from the Sun website, here.

Try installing and configuring samba or ssh.